Question
In centimeters, what is the unknown length in this right triangle?
A right triangle with side length 60 centimeters, x, and hypotenuse of 61 centimeters.
A right triangle with side length 60 centimeters, x, and hypotenuse of 61 centimeters.
Answers
GPT-4o mini
To find the unknown length \( x \) in the right triangle with one side measuring 60 centimeters and a hypotenuse measuring 61 centimeters, we can use the Pythagorean theorem:
\[
a^2 + b^2 = c^2
\]
where
- \( a \) and \( b \) are the lengths of the two legs of the right triangle,
- \( c \) is the length of the hypotenuse.
In our case:
- One leg \( a = 60 \) cm,
- The hypotenuse \( c = 61 \) cm,
- The other leg \( b = x \) (the unknown length we want to find).
Plugging the known values into the Pythagorean theorem gives us:
\[
60^2 + x^2 = 61^2
\]
Calculating \( 60^2 \) and \( 61^2 \):
\[
3600 + x^2 = 3721
\]
Now, we can solve for \( x^2 \):
\[
x^2 = 3721 - 3600
\]
\[
x^2 = 121
\]
Taking the square root of both sides to solve for \( x \):
\[
x = \sqrt{121} = 11
\]
Thus, the unknown length \( x \) is:
\[
\boxed{11} \text{ centimeters}
\]
\[
a^2 + b^2 = c^2
\]
where
- \( a \) and \( b \) are the lengths of the two legs of the right triangle,
- \( c \) is the length of the hypotenuse.
In our case:
- One leg \( a = 60 \) cm,
- The hypotenuse \( c = 61 \) cm,
- The other leg \( b = x \) (the unknown length we want to find).
Plugging the known values into the Pythagorean theorem gives us:
\[
60^2 + x^2 = 61^2
\]
Calculating \( 60^2 \) and \( 61^2 \):
\[
3600 + x^2 = 3721
\]
Now, we can solve for \( x^2 \):
\[
x^2 = 3721 - 3600
\]
\[
x^2 = 121
\]
Taking the square root of both sides to solve for \( x \):
\[
x = \sqrt{121} = 11
\]
Thus, the unknown length \( x \) is:
\[
\boxed{11} \text{ centimeters}
\]